Britain's monarch is famously above politics, but prime minister David Cameron was overheard saying Queen Elizabeth II had "purred" with happiness when he phoned her to tell her Scotland had voted to reject independence.

In New York to attend the United Nations General Assembly, TV crews accidentally picked up remarks Mr Cameron made to Michael Bloomberg, the former mayor of the city, which are likely to embarrass the Queen and the British leader.

"She purred down the line. I've never heard someone so happy," Mr Cameron, whose Conservative Party campaigned for Scotland to stay in the United Kingdom, said of the Queen, according to BBC TV and Sky News.

Mr Cameron also revealed he had been frustrated with pollsters who towards the end of the September 18 referendum suggested the outcome would be close. In the end, Scots voted 55-45 to reject independence.

"It should never have been that close. It wasn't in the end, but there was a time in the middle of the campaign when it felt...," said Mr Cameron, the microphones failing to pick up the rest of his sentence.

"I've said I want to find these polling companies and I want to sue them for my stomach ulcers because of what they put me through, you know. It was very nervous."

Mr Cameron's office and Buckingham Palace said they would not be commenting on the remarks.

The Queen said publicly after the vote she was sure Scots would be able to come together in a spirit of mutual respect after the divisions of their independence referendum.

You have no doubt been hearing a lot about the Paris Agreement and know that it pertains to climate change, but are too embarrassed at this stage to ask for an overall explanation of what it's all about.